Finitary Sets
Abstract
The diamond subset, later relevant to the characterization of finite elasticities in Chap. 8, is introduced along with various equivalent definitions. The crucial notion of a finitary set is defined using the language of Chaps. 3–6, followed by an in-depth study of finitary sets, including geometric properties and conditions that ensure a given set is finitary. An associated notion of series decomposition is given and studied, leading to four key finiteness properties of finitary sets. The notions of lattice types and minimal types, as well as related notation and concepts, are introduced. Their crucial finiteness and interchangeability properties, needed for many results in Chap. 8, conclude the chapter.
Publication Title
Lecture Notes in Mathematics
Recommended Citation
Grynkiewicz, D. (2022). Finitary Sets. Lecture Notes in Mathematics, 2316, 133-206. https://doi.org/10.1007/978-3-031-14869-9_7
